Constructing class fields over local fields
Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 3, pp. 627-652.

Let K be a 𝔭-adic field. We give an explicit characterization of the abelian extensions of K of degree p by relating the coefficients of the generating polynomials of extensions L/K of degree p to the exponents of generators of the norm group N L/K (L * ). This is applied in an algorithm for the construction of class fields of degree p m , which yields an algorithm for the computation of class fields in general.

Soit K un corps 𝔭-adique. Nous donnons une caractérisation explicite des extensions abéliennes de K de degré p en reliant les coefficients des polynômes engendrant les extensions L/K de degré p aux exposants des générateurs du groupe des normes N L/K (L * ). Ceci est appliqué à un algorithme de construction des corps de classes de degré p m , ce qui conduit à un algorithme de calcul des corps de classes en général.

DOI: 10.5802/jtnb.563
Pauli, Sebastian 1

1 Department of Mathematics and Statistics University of North Carolina Greensboro Greensboro, NC 27402, USA
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Pauli, Sebastian. Constructing class fields over local fields. Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 3, pp. 627-652. doi : 10.5802/jtnb.563. http://www.numdam.org/articles/10.5802/jtnb.563/

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